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Deterministic time–frequency representations are commonly used in signal processing, particularly in audio processing. Whilst presenting many potential advantages, their probabilistic counterparts are not widely used, essentially because of the computational load and the lack of clear interpretability of the different underlying models. However, using state space models, they have been shown recently to be equivalent to Spectral Mixtures Gaussian processes (SM-GP). This pioneer work unlocks this problem and opens the path for the development of tractable and interpretable probabilistic time–frequency analysis. In this paper, we propose a relatively simple yet a significant improvement of that work in terms of computational complexity, flexibility and practical application. To do so, we use a recent approach for covariance approximation to develop an algorithm for faster inference of SM-GP, while opting for a frequency-domain approach to hyperparameter learning. We illustrate the practical potential of our method using voiced speech data. We first show that key speech features can be accurately learned from the data. Second, we show that our method can yield better performances in denoising. [ABSTRACT FROM AUTHOR]

• Decentralised processing where only information within a localized subgraph of nodes are required. • Approximate arbitrary linear graph signal operators that require matrix inversion with sparse matrices that have low geodesic-width. • Low-computational complexity and arbitrarily small approximation error are achievable. • Application in signal denoising and signal reconstruction in graph filter banks. In the processing of signals defined over graph domains, it is highly desirable to have algorithms that can be implemented in a decentralised manner, whereby each node only needs to exchange information within a localized subgraph of nodes. The most common example is when the subgraph consist of immediate neighbors and this allows for distributed processing. Many graph signal operators, in their original forms, are not amenable to distributed processing. To overcome this deficiency, a polynomial approximation is usually applied to the original operator to yield a distributed operator which is a matrix polynomial of the graph shift matrix. This approach however is only applicable when the original operator is a function of the graph shift matrix. In this paper, we propose a generalized approach to approximate graph signal operators that are not necessary functions of the shift matrix. The key idea here is to restrict the approximated matrix inverse to have small geodesic-width so that multiplication with the small geodesic-width matrix can be implemented in a decentralised manner. Furthermore, to increase the accuracy of the approximated operator, an iterative algorithm which also has the decentralised property and low computational complexity, is proposed. We apply the proposed approach to signal inpainting and signal reconstruction in filter banks. Numerical results verify the effectiveness of the proposed algorithm. The proposed algorithms can also be used to efficiently solve linear system of equations. [ABSTRACT FROM AUTHOR]

• The rank-(Lr,Lr,1) block-term tensor decomposition (BTD) model has been attracting increasing attention in numerous application areas. • In data-streaming scenarios and/or big data applications, it is essential to be able to jointly select the model and estimate its parameters in a recursive (online/incremental) manner. • A novel approach to BTD model selection and tracking is proposed, based on the idea of imposing column sparsity jointly on the factors. • An online method of the reweighted least squares (RLS) type is developed and shown to be computationally and memory efficient and fast converging, also allowing for the model ranks to change. • Simulation results with both synthetic and real data demonstrate the effectiveness of the proposed scheme in both selecting and tracking the correct BTD model. The so-called block-term decomposition (BTD) tensor model, especially in its rank- (L r , L r , 1) version, has been recently receiving increasing attention due to its enhanced ability to represent systems and signals that are composed of block components of rank higher than one, a scenario encountered in numerous and diverse applications. Its uniqueness and approximation have thus been thoroughly studied. The challenging problem of estimating the BTD model structure, namely the number of block terms (rank) and their individual (block) ranks, is of crucial importance in practice and has only recently started to attract significant attention. In data-streaming scenarios and/or big data applications, where the tensor size grows in time or the processing can only be done incrementally, it is essential to be able to perform model selection and computation in a recursive (online/incremental) manner. In this paper, a novel approach to rank- (L r , L r , 1) BTD model selection and tracking is proposed, based on the idea of imposing column sparsity jointly on the factors and estimating the ranks as the numbers of factor columns of non-negligible magnitude. In this vein, and using a new rank-revealing batch BTD approximation algorithm as the starting point, an online method of the alternating reweighted least squares (RLS) type is developed and shown to be computationally efficient and fast converging, also allowing the model ranks to change in time. Its time and memory efficiency are evaluated and favorably compared with those of the batch approach and a recently reported online BTD scheme that is based on a-priori knowledge of the ranks. Simulation results with both synthetic and real (video) data are reported, that demonstrate the effectiveness of the proposed scheme in both selecting and tracking the correct BTD model. [ABSTRACT FROM AUTHOR]

Highlights • Highly accurate algorithm for extracting level crossing timing information from band-limited signals. • Reconstruction algorithm for highly accurate (better than 100 dB MSE) signal recovery from level crossing time stamps. • Excellent local approximations provided by chromatic derivatives and expansions allow extremely accurate signal recovery from just 2-level amplitude sampling. • Even with extremely close asymmetric two amplitude levels highly accurate signal recovery is verified with better than 100 dB MSE for audio signals from well-known datasets. Graphical abstract Abstract A novel, highly accurate signal reconstruction algorithm for signal recovery from 2-level amplitude sampling is proposed. Our method is non-iterative and exploits high fidelity local signal approximation properties of special, numerically robust differential operators known as chromatic derivatives and the associated chromatic signal expansions. Algorithms are proposed to obtain highly accurate timing information from 2-level amplitude sampling followed by signal reconstruction from thus obtained non-uniform time stamps. Numerical simulations with synthetic sinusoidal and standard speech inputs verify signal reconstruction accuracy better than 200 dB and 100 dB, respectively, in terms of the mean square error (MSE). With level crossings corresponding to two amplitude levels that are very closely placed and asymmetric (i.e., either on only the positive or the negative side of the signal), the proposed algorithm can still reconstruct synthetic and speech signals with MSE accuracies better than 175 dB and 100 dB, respectively. Experimental results with fixed-point quantized time stamps are also presented, along with a comprehensive comparison with state of the art methods in literature. [ABSTRACT FROM AUTHOR]

The concept of a mapping, which takes its values in an infinite-dimensional functional space, has been studied by the mathematical community since the third decade of the last century. This effort has produced a range of important contributions, many of which have already made their way to applied sciences, where they have been successfully used to facilitate numerous practical applications across various fields. Surprisingly enough, one particular field, which could have benefited from the above contributions to a much greater extent, still relies on finite-dimensional models and approximations, thus missing out on numerous advantages offered through adopting a more general framework. This field is image processing, which is in the focus of this study. In particular, in this paper, we introduce an alternative approach to the analysis of multidimensional imagery data based on the mathematical theory of function-valued mappings. In addition to extending various tools of standard functional calculus, we generalize the notions of Fourier and fractal transforms, followed by their application to processing of multispectral imaging data. Some applications and future extensions of this work are discussed as well. [ABSTRACT FROM AUTHOR]

This paper considers the estimation and detection problems for statistically dependent heavy-tailed signals with no closed-form probability density function (PDF). We propose two parametric PDF approximations for symmetric α -stable (S α S) distribution to be utilized in approaches based on the Maximum likelihood (ML) criterion. The nonlinear least square (LS) and curve fitting are used to compute parameters of the new formulations which are functions of the characteristic exponent. Moreover, we study binary signal detection in channels with time-dependent heavy-tailed noise modeled by S α S distribution and first order autoregressive (AR(1)) process. Using the novel PDF approximations in the ML estimator, an algorithm for model parameters estimation of the noise is initially developed. Then, new suboptimal receivers are designed through the use of the new PDF formulations and parameter estimates. Numerical results demonstrate the superiority of the proposed approximations over the existing formulations, and also good accuracy for the estimation algorithm. Additionally, it is shown that the proposed detectors operate near optimal receiver and also outperform the other suboptimal detectors, especially when α is small. [ABSTRACT FROM AUTHOR]

In this paper, we consider estimating multiple Gaussian graphs with a similar sparsity structure. Most related solving methods, such as GGL (Group graphical lasso) and FMGL (Fused multiple graphical lasso), focus on the information of the edge values, and pay few attention to the estimation based on structure information. We construct a jointly sparse penalty to encourage graphs to share a similar sparsity structure by utilizing information of the common structure across the graphs. The new objective function is neither convex nor differentiable. Combining block coordinate descent and majorization–minimization strategies, we derive a new re-weighed algorithm to solve the problem by transforming the subproblems in every iteration into convex ones. Experimental results show that the proposed algorithm outperforms FMGL and GGL when the sparsity structure is similar but the edge values are not. [ABSTRACT FROM AUTHOR]

3D human motion tracking has received increasing attention in recent years due to its broad applications. Among various 3D human motion tracking methods, the particle filter is regarded as one of the most effective algorithms. However, there are still several limitations of current particle filter approaches such as low prediction accuracy and sensitivity to discontinuous motion caused by low frame rate or sudden change of human motion velocity. Targeting such problems, this paper presents a full-body human motion tracking system by proposing exemplar-based conditional particle filter (EC-PF) for monocular camera. By introducing a conditional term with respect to exemplars and image data, dynamic model is approximated and used to predict current states of particles in prediction phase. In update phase, weights of particles are refined by matching images with projected human model using a set of features. This method retains advantages of classic particle filters while increases prediction accuracy by replacing the smooth motion model with exemplars-based dynamic model which constrains evolved particles within an area closer to true state. Therefore, tracking robustness to discontinuous motion is improved such as under conditions of sudden change in motion velocity or using low-frame rate cameras. To verify the effectiveness and efficiency of the proposed algorithm, a variety of datasets are selected for testing and the results are also compared with the state-of-the-art methods in this domain. [ABSTRACT FROM AUTHOR]

Abstract: We study vertex selection in the presence of multiple graphs associated with a vertex set V representing an online community. First, we formulate a collection of Markov chains on the graph ensemble and describe the characteristics of the associated mean hitting times on V. Then, we design a branch and bound optimisation technique for computing the subset of vertices A that exhibits the smallest hitting time cost across the multi-graph, given a constraint on the volume of A. The complexity of the branch and bound technique limits its application to medium-size graphs. Thus, we formulate a greedy optimisation method for computing a close approximation to the optimal subset at lower complexity, which can be implemented in a decentralised way, for further complexity reduction. We prove that the objective function under consideration is supermodular and monotonic, which guarantees near-optimal solutions for the greedy method. This is verified in our numerical experiments that compare its performance to that of the branch and bound technique, on smaller size graphs. The experiments also examine the hitting-time trade-off across the multi-graph that our optimisation exhibits, governed by the sampling cost factors λ j associated with each graph layer G j . Relative to conventional community graph centrality methods for vertex selection, we demonstrate a substantially lower sampling (network) cost and higher data dissemination rate, on actual Facebook and Internet topology data. The generality of our framework allows for its application to information retrieval, from a collection of items represented by a multi-graph. Here, we demonstrate higher semantic consistency over state-of-the-art single-graph methods, on the popular DBLP data set. [Copyright &y& Elsevier]

Abstract: The area of blind system identification using Higher-Order-Statistics has gained considerable attention over the last two decades. This paper, motivated by the recent developments in sparse approximations, proposes new algorithms for the blind identification and order determination of sparse systems. The methodology used relies on greedy schemes. In particular, the first algorithm exploits a single step greedy structure, while the second improves performance using a threshold-based selection procedure. Finally, the proposed algorithms are tested on a wide range of randomly generated channels and different output signal lengths. [Copyright &y& Elsevier]

Abstract: We show that the polynomial unbiased finite impulse response (UFIR) functions derived by Shmaliy establish a new class of a one-parameter family of discrete orthogonal polynomials (DOP). The most noticeable distinction of these polynomials with respect to the classical Meixner, Charlier, Hahn, and Krawtchouk DOP is dependence on only one parameter—the length of finite data. This makes them highly attractive for L-order blind fitting and analysis of informative processes. Properties of the UFIR polynomials are considered in detail along with the moments and recurrence relation. Examples of applications are given to blind approximation and phoneme pitch analysis. [Copyright &y& Elsevier]

Abstract: This paper studies the design of FIR filter with low group delay, where the desired phase response is not being approximated. It is formulated as a constrained optimization problem, which is then solved globally. Numerical experiments show that our design method can produce a filter with smaller group delay than that obtained by the existing convex optimization method used in conjunction with a minimum phase spectral factorization method under the same design criteria. Furthermore, our formulation offers us the flexibility for the trade-off between the group delay and the magnitude response directly. It also allows the feasibility of imposing constraints on the group delay. [Copyright &y& Elsevier]

Abstract: Information theoretic criteria such as mutual information are often used as similarity measures for inter-modality image registration. For better performance, it is useful to consider vector-valued pixel features. However, this leads to the task of estimating entropy in medium to high dimensional spaces, for which standard histogram entropy estimator is not usable. We have therefore previously proposed to use a nearest neighbor-based Kozachenko–Leonenko (KL) entropy estimator. Here we address the issue of determining a suitable all nearest neighbor (NN) search algorithm for this relatively specific task. We evaluate several well-known state-of-the-art standard algorithms based on k-d trees (FLANN), balanced box decomposition (BBD) trees (ANN), and locality sensitive hashing (LSH), using publicly available implementations. In addition, we present our own method, which is based on k-d trees with several enhancements and is tailored for this particular application. We conclude that all tree-based methods perform acceptably well, with our method being the fastest and most suitable for the all-NN search task needed by the KL estimator on image data, while the ANN and especially FLANN methods being most often the fastest on other types of data. On the other hand, LSH is found the least suitable, with the brute force search being the slowest. [Copyright &y& Elsevier]

Abstract: To estimate geometrically regular images in the white noise model and obtain an adaptive near asymptotic minimaxity result, we consider a model selection based bandlet estimator. This bandlet estimator combines the best basis selection behavior of the model selection and the approximation properties of the bandlet dictionary. We derive its near asymptotic minimaxity for geometrically regular images as an example of model selection with general dictionary of orthogonal bases. This paper is thus also a self-contained tutorial on model selection with orthogonal bases dictionary. [Copyright &y& Elsevier]

Abstract: In this work we present a new greedy algorithm for sparse approximation called LocOMP. LocOMP is meant to be run on local dictionaries made of atoms with much shorter supports than the signal length. This notably encompasses shift-invariant dictionaries and time–frequency dictionaries, be they monoscale or multiscale. In this case, very fast implementations of Matching Pursuit are already available. LocOMP is almost as fast as Matching Pursuit while approaching the signal almost as well as the much slower Orthogonal Matching Pursuit. [Copyright &y& Elsevier]

Abstract: Two main drawbacks can be stated in the alternating least square (ALS) algorithm used to fit the canonical decomposition (CAND) of multi-way arrays. First its slow convergence caused by the presence of collinearity between factors in the multi-way array it decomposes. Second its blindness to Hermitian symmetries of the considered arrays. Enhanced line search (ELS) scheme was found to be a good way to cope with the slow convergence of the ALS algorithm together with a partial use of the Hermitian symmetry. However, to our knowledge, required equations to perform the latter scheme are only given in the case of third and fifth order arrays. Therefore, our first contribution consists in generalizing the ELS procedure to the case of complex arrays of any order greater than three. Our second contribution is another improvement of the ALS scheme, able to profit from Hermitianity and positive semi-definiteness of the considered arrays. It consists in resorting to the CAND first of a third order array having one unitary loading matrix and second of several rank-1 arrays. An iterative algorithm is then proposed alternating between Procrustes problem solving and the computation of rank-one matrix approximations in order to achieve the CAND of the third order array. [Copyright &y& Elsevier]

Abstract: The CHaracteristic-function-Enabled Source Separation (CHESS) method for independent component analysis (ICA) is based on approximate joint diagonalization (AJD) of Hessians of the observations'' empirical log-characteristic-function, taken at selected off-origin “processing points”. As previously observed in other contexts, the AJD performance can be significantly improved by optimal weighting, using the inverse of the covariance matrix of all of the off-diagonal terms of the target-matrices. Fortunately, this apparently cumbersome weighting scheme takes a convenient form under the assumption that the mixture is already “nearly separated”, e.g., following some initial separation. We derive covariance expressions for the Sample-Hessian matrices, and show that under the near-separation assumption, the weight matrix takes a nearly block-diagonal form, conveniently exploited by the recently proposed WEighted Diagonalization using Gauss itErations (WEDGE) algorithm for weighted AJD. Using our expressions, the weight matrix can be estimated directly from the data—leading to our WeIghTed CHESS (WITCHESS) algorithm. Simulation results demonstrate how WITCHESS can lead to significant performance improvement, not only over unweighted CHESS, but also over other ICA methods. [Copyright &y& Elsevier]

Abstract: In this paper, state estimation problem for discrete-time Markov jump linear systems is considered. First, three equalities are proposed. Next, they are applied to the state estimation problem of considered systems so that a novel suboptimal algorithm in the sense of minimum mean-square error estimate is obtained where the computation and storage load of the suboptimal algorithm is not ever-increasing with the length of the noise observation sequence. The proposed algorithm and the suboptimal adaptive algorithm proposed in are all based on a truncated approximation strategy. However, compared with the algorithm of , the proposed algorithm requires much less approximations. Computer simulations are carried out to evaluate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

• Take residual network to design waveform for MIMO radar transmit beampattern and get a better performance. • The proposed methods can solve the problem directly and don't need to synthesis waveform covariance matrix. • The proposed methods can also suppress cross-correlation sidelobes while keep a good performance on beampattern matching. • The proposed methods with residual network provide some new ideas for the constant modulus waveform design in MIMO radar. This paper considers the design of MIMO radar waveform to approximate a desired beampattern while minimizing the cross-correlation sidelobes under the constant modulus constraint. Since the resulting problem is high-dimensional and non-convex (also known as NP-hard), it is extremely difficult to find the global optimization solution through polynomial-time algorithms. A possible methodology is to invoke heuristic iterative optimization algorithms to find an approximation solution by providing as small an beampattern matching error as possible. Recently, we notice that the residual neural network is naturally a nonlinear system, which is very suitable for solving the above problem. In this respect, for the first time, we introduce the residual neural networks to the MIMO radar waveform design for transmit beampattern. More precisely, we formulate two transmit beampattern optimization problems, then convert them into the univariate optimization problems. Finally, we solve them with the designed residual neural network, respectively. Numerical results show that the proposed method can obtain the better beampattern performance over the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

• We design a novel deep neural network that unfolds an iterative algorithm for sparse approximation from 1-bit measurements. The resulting network architecture resembles that of deep residual learning, implying that the model has the potential to be deeply trained. • We show that DeepFPC offers higher signal reconstruction accuracy and speed than the iterative FPC-l1 algorithm. • We apply DeepFPC in the DOA estimation problem and show that it outperforms the state-of-the-art FPC-l1 and deep convolution network (DCN) methods. In this paper, we introduce a novel deep neural network, coined DeepFPC, and investigate its application to tackling the problem of direction-of-arrival (DOA) estimation. DeepFPC is designed by unfolding the iterations of the fixed-point continuation algorithm with one-sided ℓ 1 -norm (FPC-ℓ 1), which has been proposed for solving the 1-bit compressed sensing problem. The network architecture resembles that of deep residual learning and incorporates prior knowledge about the signal structure (i.e., sparsity), thereby offering interpretability by design. Once DeepFPC is properly trained, a sparse signal can be recovered fast and accurately from quantized measurements. The proposed model is then applied in DOA estimation and is shown to outperform state-of-the-art solutions; namely, the iterative FPC-ℓ 1 algorithm and the deep convolution network (DCN) model. [ABSTRACT FROM AUTHOR]